The present invention concerns printed circuits formed by standard technologies and concerns the reduction of losses appearing in these circuits.
More specifically, the invention concerns micro-strip inductors for Microwave Monolithic Integrated Circuits (MMIC) based on silicon substrates or other lossy substrates.
Inductor coils constitute an important group of components for MMIC""s and inductor quality is often a limiting factor for the performance of such MMIC circuits that typically operate in the frequency band of up to 10 GHz.
Inductors for these applications may be characterised by the quality factor, Q, which can be defined as:
Q=xcfx89L/r,
where xcfx89 is the circular frequency, L is the inductance and r is the parasitic resistance.
The Q-factor is normally limited by three types of losses, namely by losses in the substrate, losses in the metal strips and by the losses relating to the radiation of electromagnetic energy from the circuit. However, the radiation losses are normally negligible in comparison with the other two types of losses.
Substrate losses are normally dominant where the resistivity of silicon is smaller than 1-10 xcexa9xc2x7cm. For substrate resistivities above 100 xcexa9xc2x7cm the losses in the metal strips become dominant.
Many proposals have been put forward in the prior art for reducing losses in inductors on silicon based substrates. One way of doing this is to reduce the substrate losses.
Substrate Losses
In prior art document xe2x80x9cLarge suspended Inductors on Silicon and their Use in a 2 xcexcm CMOS RF Amplifierxe2x80x9d, by Chang et al., IEEE Electron Device Letters, Vol. 14, No. 5, May 1993, pp. 246, a suspended inductor has been proposed. The inductor comprises segments of strips, for which the underlying substrate has been removed thereby leaving the section freely suspended in the air. Accordingly, substrate currents in the immediate vicinity of the section of the strips are avoided. According to this document, the suspension may be achieved by selectively etching out the silicon, leaving the inductor encased in a suspended oxide layer attached at four corners to the rest of the silicon IC.
In U.S. Pat. No. 5,539,241, a suspended inductor is shown having a similar structure to the suspended inductor mentioned above. According to this document a membrane dielectric layer is formed on the silicon substrate for preventing an anisotropic backside etch during removal of the substrate underneath the inductor.
Strip Losses
A reduction of strip losses has also been suggested in the prior art.
According to prior art document xe2x80x9cMicrowave Inductors and Capacitors in Standard Multilevel Interconnect Silicon Technologyxe2x80x9d, Burghartz et al, IEEE Transactions on Microwave Theory and Techniques, Vol.44, No. 1, January 1996, pp. 100-104, a multi-layer inductor has been suggested, which reduces the above losses. The multi-layer inductor disclosed in this document comprises conductive via array shunts arranged between the layers forming the coil of the inductor for enhancing the current carrying cross-section of the inductor. Thereby, the current density and hence the effective ohmic resistance of the inductor coil has been lowered.
One important factor, which might reduce the effective current carrying area of the strips, is the so-called current crowding effect according to which the current in a strip is non-uniformly distributed due to the generation of eddy currents in the strips.
The implication of the current crowding effect on inductors has for instance been mentioned in prior art document xe2x80x9cA 1.8 GHz Low-Phase-Noise CMOS VCO Using Optimised Hollow Spiral Inductorsxe2x80x9d by Craninckx et al. IEEE Journ. Solid State Circuits, Vol.32, No.5, 1997, pp. 736-744. In this document, it is found that especially the inner turns of the coils are affected by losses due to eddy currents causing a non-uniform current distribution. As a general recommendation, it has been proposed that spiral coils should have narrow strips and a free inner area of the coil.
Radiation Losses
As will be readily understood, the Q-factor of an inductive coil depends not only on the ohmic losses, but also on the inductance and hence on the geometry of the coil.
For instance, it is known that 90xc2x0 bends (c.f. xe2x80x9cEnd-Effects in Quasi-TEM Transmission linesxe2x80x9d by Getsinger, IEEE Trans. Microwave Theory Techn. Vol. 41, pp. 666-672, 1993) in the strips act like xe2x80x9copen circuitsxe2x80x9d for the currents whereby negative inductances are introduced due to the stray magnetic fields. This phenomenon leads to a substantial reduction of the total inductance and of the Q-factor of the coil.
In FIG. 3 the Q-factor relating to two strips, a) being straight and b) comprising a 90xc2x0 bend, has been indicated as a function of the frequency. The illustration is based on experiments carried out by the inventors. The experiments were based on strips having a mean length of 300 xcexcm, a strip width of 30 xcexcm and strip thickness of 1.5 xcexcm, whereby the substrate was 300 xcexcm thick Si (20 xcexa9m). The above illustration does not form part of the prior art.
In the following, the current crowding effect shall be dealt with briefly.
FIG. 1 shows the outline of a conventional coil and FIG. 2, which was produced by the inventors, shows a cross section of the coil shown in FIG. 1 and a schematic illustration of the current distribution in a cross-section of the strip of the coil shown in FIG. 1. It appears that the current density is highest at the edges of the strip and that the current density is highest in the inner turns of the coil.
FIGS. 4 and 5, which were produced by the inventors, relates to a computer-simulated analysis (Momemtum(copyright) by Hewlett Packard(copyright) of a circuit being modelled with the strips being formed directly on a lossy substrate. FIG. 4 is a schematic illustration of the current distribution on a straight strip and showsxe2x80x94in compliance with FIG. 2xe2x80x94that current crowding is effected at the edges of the strip, whereby the current density is higher (indicated by h) than at the central portion of the strip.
FIG. 5 is a schematic illustration of the current distribution for a strip having a 90xc2x0 bend and demonstrates that the current density at the edges of the strips and especially at the internal edge of a 90xc2x0 bend, is higher than at the central portions of the strip.
FIG. 6a which shows more accurately the variation in the current density according to the lateral position of the strip along line Axe2x80x94A in FIG. 4 for a typical configuration. It is seen that the current density is highest at the edges and lowest at central portions of the strip. FIG. 6b is similar to FIG. 6a but relates to FIG. 5 along line Bxe2x80x94B. The current density is highest at the internal bend.
It should be noted that the current density would depend on many factors such as dielectric properties of the substrate, the thickness of the substrate, the strip width, the frequency applied etc. Moreover, it should be noted that the current density varies along the edges of the strip shown in FIG. 5 as well as on the central portions. However, the general pattern is as shown in FIGS. 4, 5, 6a and 6b. More accurate results for a given strip configuration can be found using for instance simulation tools as indicated above.
The current crowding effect increases the ohmic losses and reduces the Q-value of the inductive properties of the strip.
One object of the present invention is to accomplish a new and more effective design for standard micro-strip circuits based on lossy substrates.
This object has been achieved by subject matter whereby a intermediate member having a low dielectric constant or being conductive is formed under the strip, the intermediate member having a minimum lateral extension being less that the width of the strip.
The disclosed micro-strip circuit leads to a reduction in locally appearing areas of high current densities as compared to the prior art structures mentioned above. The intermediate member forces currents to the parts of the strips being located over the intermediate member, thereby rendering the cross-sectional distribution of the current in the strips more uniform. Consequently, the effective current carrying area of the strip increases such that a reduction of the strip losses is accomplished.
The invention may be applied for single layer technology, whereby the circuit is being printed directly on a lossy substrate. This solution is further advantageous in that the substrate losses are reduced.
The invention may also be applied in multi-layer technology, whereby a first circuit layer is provided on a lossy substrate and more layers are provided on top of these, each layer being separated by respective dielectric layers.
It is a further object to achieve further reductions in losses, especially substrate losses appearing at the bends of the strips.
The micro-strip circuits according to the invention can be produced very economically, both in large and small-scale production.
Further advantageous features will appear from the remaining dependent claims and the following detailed description.